# Michael Lugo

 8,385 Reputation 3834 views

## Registered User

 Name Michael Lugo Member for 3 years Seen 6 mins ago Website Location Oakland, CA, USA Age 29
I'm a lecturer in statistics at Berkeley. I earned my PhD at the University of Pennsylvania, working in combinatorics and probability. In particular I'm interested in what large random structures look like. I think generating functions are awesome, which is probably pretty clearly reflected in the questions I answer.
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# Questions

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### Teaching statements for math jobs?

nov 30 09 at 20:31 Deane Yang 12.6k13380

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### Why are powers of $\exp(\pi\sqrt{163})$ almost integers?

may 18 12 at 9:12 Didier Piau 4,19311015

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### Is there a combinatorial reason that the (-1)st Catalan number is -1/2?

feb 19 10 at 3:39 Jacques Carette 6,71711435

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### If you break a stick at two points chosen uniformly, the probability the three resulting sticks form a triangle is 1/4. Is there a “nice” proof of this fact?

mar 22 at 18:21 Shaswata 1

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### What relationship, if any, is there between the diameter of the Cayley graph and the average distance between group elements?

apr 13 11 at 5:37 Denis Chaperon de LauziÃ¨res 2,19428

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### When are some products of gamma functions algebraic numbers?

dec 3 09 at 21:18 Felipe Voloch 16.6k23661

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### What’s the probability that k + n^2 is squarefree, for fixed k?

mar 1 10 at 22:53 Bjorn Poonen 14.2k24775

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### How many pairs (M, N) of sets of size n have M + N = {0, 1, …, n^2-1}?

apr 8 10 at 13:47 D. Savitt 1,8911518

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### How can I generate random permutations of [n] with k cycles, where k is much larger than log n?

jun 3 10 at 23:15 James Martin 1,596414

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### An integral that somehow equals pi^2/6 and involves dilogarithms?

apr 5 11 at 2:47 Tom Dickens 69348

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# Tags

 co.combinatorics× 37 nt.number-theory× 35 pr.probability× 28 soft-question× 17 geometry× 11 ca.analysis-and-odes× 11 graph-theory× 10 st.statistics× 9 prime-numbers× 9 big-list× 9 asymptotics× 9 gr.group-theory× 7 examples× 6 algorithms× 6 reference-request× 5 mg.metric-geometry× 5 mathematics-education× 5 tag-removed× 4 permutations× 4 intuition× 4 finite-groups× 4 analytic-number-theory× 4 polynomials× 3 linear-algebra× 3 ho.history-overview× 3 generating-functions× 3 ds.dynamical-systems× 3 career× 3 teaching× 2 taylor-series× 2 publishing× 2 order-theory× 2 modular-forms× 2 matrices× 2 markov-chains× 2 latex× 2 journals× 2 it.information-theory× 2 gt.geometric-topology× 2 fa.functional-analysis× 2 cv.complex-variables× 2 convex-polytopes× 2 combinatorial-game-theory× 2 calculus× 2 books× 2 big-picture× 2 ag.algebraic-geometry× 2 writing sums-of-squares spherical-geometry

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